I'm thinking board. Ours was doing weird things when we bought the trailer, running for very short intervals, then restarting minutes later. Like you I replaced the thermostat and ECO with no improvement. A new board cleared it right up.
I want to say the one for ours was $125 or so...but it's been a while.
1995 Airstream Classic 30' Excella 1000
2014 Ram 2500 Crew Cab with Cummins 6.7L Diesel
Sold but not forgotten: 1991 Airstream B190
Sold: 2006 F-250 6.0L Powerstroke Supercab